Solve for $x$, $ -\dfrac{7}{2x - 2} = -\dfrac{x}{3x - 3} + \dfrac{3}{4x - 4} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2x - 2$ $3x - 3$ and $4x - 4$ The common denominator is $12x - 12$ To get $12x - 12$ in the denominator of the first term, multiply it by $\frac{6}{6}$ $ -\dfrac{7}{2x - 2} \times \dfrac{6}{6} = -\dfrac{42}{12x - 12} $ To get $12x - 12$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ -\dfrac{x}{3x - 3} \times \dfrac{4}{4} = -\dfrac{4x}{12x - 12} $ To get $12x - 12$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ \dfrac{3}{4x - 4} \times \dfrac{3}{3} = \dfrac{9}{12x - 12} $ This give us: $ -\dfrac{42}{12x - 12} = -\dfrac{4x}{12x - 12} + \dfrac{9}{12x - 12} $ If we multiply both sides of the equation by $12x - 12$ , we get: $ -42 = -4x + 9$ $ -42 = -4x + 9$ $ -51 = -4x $ $ x = \dfrac{51}{4}$